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348                               CHEMICAL ENGINEERING
We believe the discrepancy is due to the following points which are not taken into account in these various formulas. First, if we assume we have a continuous agitation system made up of four agitators, in which we are leaching pyrites cinders with 10 per cent sulphuric acid the system will become balanced and the strength of the sulphuric acid in the four tanks will become constant. For purposes of comparison, we will assume this to be:
First, tank 9 per cent H2S04; second, tank 5 per cent H2S04; third, tank 3 per cent H2S04; fourth, tank Jú P^ cent H2S04.
Now, assuming a detention period of 24 hr. is necessary the average period in each *ank would be 6 hr. Also the rate of dissolution as shown by Fig. 1, is not a straight ine curve. (Figure 1 is plotted against time but in intermittent tests of this kind the solution is becoming weaker and is the real variable while time is only the apparent variable.) The first tanks of this system would then be working on the steep part of this curve while the last tank only would be on the flat portion.
Now, as pointed out before, 6 hr. is the average time of detention in each tank but some material will be retained in the first tank as long as 12 hr., but the rate of extraction throughout this period will be greater than if it were carried on by intermittent agitation due to the fact that the strength of the solution remains constant. This rate may be gotten by drawing a tangent to the curve at the point corresponding to the concentration of this first tank.
Second, one other point not brought out in these calculations is that we seldom obtain a 100 per cent extraction in commercial operations and usually aim at a point in the curve before it flattens out. If our leaching experiments gave us a curve similar to Fig. 1, we might aim for a 94 per cent extraction. A 100 per cent extraction, of course, is possible, but requires a longer contact than we would ordinarily be willing to provide. However, in continuous agitation we will obtain a higher extraction on some material which will offset a part of the loss due to the low extraction on material leaving the system prematurely.
Finally, to sum up these two effects, we believe the "short circuiting" of material in continuous agitation systems is largely offset by a portion of the material being dissolved at a rate higher than that obtained by intermittent systems and to a higher extraction obtained on material remaining in the system longer than the average period.
By counter current dissolution is meant a process of dissolving one substance in another by bringing them in contact either intermittently or continuously in such a way that their respective content of the soluble compound varies in a direct proportion. A specific case would be the leaching of beets in the manufacture of beet sugar. A battery of 12 or more large cylindrical tanks is used. They are connected in series so that water fed into the last tank flows through the other 11. When all the sugar has been extracted from the beets in the last tank this tank is cut out of the circuit and a fresh tank added at the other end. In this way the beets containing the least sugar come in contact with solution in a like condition.
This system is used in practically every leaching operation practiced on a large scale and effects very material savings in the amount of liquor used and solute lost over completed leaching of each tank. This system may readily be applied to all the ordinary methods of leaching and washing solids such as dccantatiori; filtration; or lixiviation, and the deciding factor regarding the method to be adopted is ordinarily the physical nature of the solids to be treated.1
1 See p. 286 for a further discussion of this point.